Margaret Thatcher was frequently called a monster or a zealot, but “The Iron Lady” comes up with an entirely unexpected word for her: woman.

Sincerely directed by one woman (Phyllida Lloyd, who did “Mamma Mia!”) and smartly written by another (Abi Morgan), the film stars an unsurpassable Meryl Streep, whose ability to empathize with her characters has never been more gloriously impassioned than it is in this titanic performance.

Anchored in Thatcher’s declining years, marked by strokes and dementia, “The Iron Lady” is a memory play in which, puttering unsteadily about her home, the aged Thatcher chats with her long-dead husband Denis (a jolly Jim Broadbent) and recalls her glory days.

Margaret Roberts was a shy grocer’s daughter with a double handicap — she was female and middle-class. Eagerly attending a speech given by her father, who became a conservative mayor in their small town, young Margaret is given dirty dishes to wash. Later, at a dinner with party authorities, she and the other ladies are asked to leave the room so the men can discuss importan t matters. Upon being elected, in 1959, she drives to Parliament, trying not to notice her pleading twins running after her. She sweeps toys off the car seat and notices there is lipstick on her teeth.

I don’t think a male screenwriter would have caught much of this disarming and very human detail. Just the shot of Thatcher’s pumps amid the wingtips in Parliament tells us all about how she literally changed the look of that Old Boy Club; in another amusing scene, she literally lights up a room, after a power failure. At its most moving, “The Iron Lady” shows us how one person, however unlikely, can change the world.

Near the middle, the story grows irresistibly rousing: When a fellow M.P. opines that “the lady doth screech too much,” instead of crying sexism, she huddles with speech counselors who teach her to lower her pitch. The contrast with “The King’s Speech” is illuminating, and much to the detriment of last year’s shallow crowd-pleaser. Bertie was a lackluster fellow who became a figurehead through no doing of his own, showed no real leadership and managed merely, eventually, to spit out a banal address.

In the 1970s, when the two main parties disagreed only on whether to be quietly socialist or loudly socialist, Thatcher scrambled from nowhere to the top, rammed backbones into her resisting colleagues and reversed the country’s course.

“It’s time to put the Great back in Great Britain,” she announces, to a country seized by strikes. Garbage Alps formed in the street. Dead bodies remained above ground, hostage to gravediggers’ unions.

Even as the country added wealth as never before and Thatcher was nearly killed by an IRA bomb, she was eventually forced out of office by her own party. The scene that illustrates why is spellbinding: In a cabinet meeting, Thatcher stands firm on principle (that all citizens should pay a tax in return for public services), then ridicules staff for giving her a typo-laden policy draft, then throws everyone out. Her resolve may be ferrous, but as Streep magnificently plays the scene, Thatcher seems surprised by herself, as though she knows she has strayed into self-parody. All great leaders are stubborn. Often it is their undoing.

Streep’s range in capturing Thatcher’s many sides — affectionate wife, uncertain outsider, decisive military commander, confused elder — marks this performance a standout even by her standards. She isn’t doing a broad parody that makes you notice the acting. She simply vanishes behind the Iron Lady (as the Soviet press dubbed Thatcher).

And the voice: uncanny.

It’s a bit unfair of the movie to devote about a third of its screen time to Thatcher’s decline, but this choice softens her, making the 20th century’s most consequential woman more human and approachable.

This really isn’t the time for “The Iron Lady.” We find it easier to think of leaders as harmless celebrities (“The Queen,” “The King’s Speech”) or gentle martyrs (“Milk”) or disgraced tyrants (“Frost/Nixon,” “J. Edgar”). Fiercely contrarian Thatcherism, though, continues to challenge us today. Like the Iron Lady, “The Iron Lady” is an argument waiting to happen. That makes it a fitting tribute.